Metamath Proof Explorer


Theorem bj-nfs1

Description: Shorter proof of nfs1 (three essential steps instead of four). (Contributed by BJ, 2-May-2019) (Proof modification is discouraged.)

Ref Expression
Hypothesis bj-nfs1.nf
|- F/ y ph
Assertion bj-nfs1
|- F/ x [ y / x ] ph

Proof

Step Hyp Ref Expression
1 bj-nfs1.nf
 |-  F/ y ph
2 bj-nfs1t2
 |-  ( A. x F/ y ph -> F/ x [ y / x ] ph )
3 2 1 mpg
 |-  F/ x [ y / x ] ph